How this instrument works
Percentage change measures how far a value moved from where it started, and it does that by fixing the old value as the base of the calculation: (new − old) ⁄ old × 100. Because the denominator is always the earlier reading, the measure is not symmetric — reverse which figure you call old and which you call new, and the percentage itself changes size, not just its sign. That single design choice is what separates this instrument from two look-alike measures. Percentage difference instead divides by the average of the two values, treating them as equal partners rather than a before-and-after pair. A percentage point, meanwhile, is not a ratio at all — it is a plain subtraction between two numbers that were already percentages, the way an interest rate moving from 4% to 6% is a two-point rise, not a fifty-percent one.
The shape of the formula follows from what 'percent' means: a rate out of 100, relative to some reference amount. Take the raw distance moved, new minus old, and express it as a fraction of the reference amount, old, then scale that fraction by 100 to read it in percent instead of a decimal. Because old sits in the denominator, the formula breaks down exactly when old is zero — there is no base left to measure against, so this sheet declines to compute rather than reporting a false zero or an undefined infinity. That same denominator is why a loss and its recovery are never equal in percentage terms: fall from 100 to 50, a 50% drop, and climbing back from 50 to 100 is not another 50% — it takes a full 100% gain, since the second calculation now divides by the smaller number.
The sign carries meaning on its own: a positive result is a rise, a negative one a fall, with no separate label needed. The measure is also scale-free — multiply both the old and new figures by the same factor and the percentage change is untouched, because that factor cancels between numerator and denominator. Going from 50 to 75 and going from 50,000 to 75,000 are, by this formula, identically a 50% increase, which is exactly the property that lets percentages compare moves of wildly different sizes on one common scale.
- Enter the starting figure into Old value — the number every result is measured against.
- Enter the later or comparison figure into New value.
- Read Percentage change: a positive figure marks a rise, a negative one a fall, both scaled against Old value.
- To check the reverse move, swap the two entries — the size of the percentage will not match the original, only its sign flips predictably.
Worked example — a rise from 50 to 75
A reading starts at an old value of 50 and is later checked at a new value of 75. Percentage change divides the move by where it started: (75 − 50) ⁄ 50 × 100 = 25 ⁄ 50 × 100 = 50%. Every part of that arithmetic uses the earlier figure, 50, as the base — the 25-unit gain is scaled against the smaller number, which is exactly why the increase reads as a full 50%.
Run the same two figures in reverse and the size changes, even though the move still covers the identical 25 units: (50 − 75) ⁄ 75 × 100 = −25 ⁄ 75 × 100 ≈ −33.3%, not −50%. The denominator switched from 50 to 75, so the identical absolute gap now reads as roughly two-thirds the size in percentage terms. That asymmetry is not a quirk of this particular pair of numbers — it is guaranteed by the formula itself, since percentage change always divides by wherever the value started, never by wherever it ended up.
Questions
Why does going from 75 to 50 read as about −33.3% and not −50%?
Because percentage change always divides by the starting value, and the starting value switches when the direction reverses. Going up, (75 − 50) ⁄ 50 × 100 = 50%. Going back down, (50 − 75) ⁄ 75 × 100 ≈ −33.3%, since the same 25-unit gap is now measured against the larger number 75 rather than 50. The absolute gap stayed identical; only the base changed.
How is percentage change different from percentage difference?
Percentage change treats the two numbers as a before-and-after pair and divides the gap by the earlier value, old, so the result depends on which figure you call old and which you call new. Percentage difference instead divides by the average of the two values, giving one symmetric figure regardless of order — suited to comparing two independent measurements rather than tracking a single value's move over time.
How is percentage change different from a percentage point change?
Percentage change is a computed ratio that always requires dividing by the old value. A percentage point change is not a ratio at all — it is plain subtraction between two numbers that are already percentages. An interest rate rising from 4% to 6% moved 2 percentage points, but in percentage-change terms that same move is a 50% increase, since (6 − 4) ⁄ 4 × 100 = 50. Both descriptions are correct; they answer different questions.
Why does the calculator refuse to compute when Old value is 0?
Because the formula divides by old, and dividing by zero has no defined result. A value that starts at 0 has no meaningful base to measure a percentage against — any nonzero new value would represent an infinite relative increase, which is not a usable figure. This sheet marks the input invalid rather than returning zero or a fabricated number.
Why does a 50% drop need more than a 50% rise to undo it?
Because each direction divides by a different base. Dropping from 100 to 50 is −50%, since 50 is being compared to 100. Climbing back from 50 to 100 divides by the now-smaller 50, so the identical 50-unit gain reads as (100 − 50) ⁄ 50 × 100 = 100%, not 50%. The lower a value falls, the larger the percentage gain needed to fully recover it.
Can Old value or New value be negative?
Yes, and the formula still runs, though the result needs careful reading. A move from −20 to −10 gives (−10 − (−20)) ⁄ −20 × 100 = 10 ⁄ −20 × 100 = −50%, a negative reading even though −10 sits closer to zero — an improvement. Whenever Old value is negative, a positive percentage change can describe a numerically worse outcome, so check the actual direction of the numbers rather than reading the sign as always 'better' or 'worse.'